He was the husband of Maria dalle Carceri, heiress of a sixth of Euboea and widow of Albert Pallavicini, and co-governed her half of the marquisate of Bodonitsa until his death.
After Albert Pallavicini's death in 1311, Bodonitsa was divided between his wife Maria and his daughter Guglielma.
Cornaro was sought out by Maria in order to defend her and her daughter's rights to Bodonitsa in light of the recent Battle of Halmyros, which had completely upended the political structure of Frankish Greece.
He had to weather an invasion by the Catalan Company and the Duchy of Athens under Alfonso Fadrique.
He was constrained to pay an annual tribute of four destriers to the vicar general of Athens.